This module compares random and quasi-random sequences by plotting in two dimensions sequences of pairs of numbers of each type. For Monte Carlo integration and a variety of other applications, random numbers are used to sample within some geometric domain. In some cases it may be more important to achieve approximately uniform coverage of the domain than for the sampling to be truly random. Quasi-random sequences, also known as low-discrepancy sequences, are carefully constructed to spread approximately uniformly over a given domain while still maintaining some appearance of randomness. Hence, quasi-random sequences may sometimes be more appropriate than truly random sequences.
This module plots a sequence of random points on the left and a sequence of quasi-random points on the right. The user adds points to the plots by clicking Add Points. The user can select how many points are added to the graph with each click of the button, controlling how quickly the graphs fill in with points. Clicking Reset clears the graphs and resets the quasi-random sequences. The pseudorandom sequence used to generate the points on the left is the linear congruential generator used in Java's Math.random( ) function. Menus allow the user to select how the quasi-random points are generated:
For either Halton sequences or Sobol sequences, the user chooses a
sequence for each of the coordinates in the plane. Each coordinate
sequence assigns the jth number of the quasi-random sequence to
its coordinate in the jth point in the sequence of points,
regardless of whether the same sequence is chosen for both
coordinates. Thus if the same sequence is chosen for both coordinates,
every point will lie on the line
References:
Developers: Evan VanderZee and Michael Heath